Sobre el teorema de interpolación de borel en espacios de hilbert

Let X be a real Hilbert space. If Ao is a real number and Am is a real symmetric and continuous m-form defined on Xm, m = 1, 2, ... , we construct a real function j on X of class C∞ such that f(m) is bounded in the bounded sets of X, f(m)(0) = Am, m = 0, 1, 2, ... , and f is analytic in X\{0}.